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Talk:2017 Spring Event/@comment-31708752-20170410092035
Edit: While still unsure, I now think the 2.65 model (lanterns/tree) is more likely to be correct than the 2.45 model. Or even if not, I think the 2.7 # previously used is more likely to be closer to the true number than 2.45, so math using 2.7 in other posts here should be fine. Mathy stuff farther down 2 paragraph TL;DR: Bronze is better for average cost of special. You will get about 10 specials from bronze for every 9 from gold. Bronze and gold are almost identical for blossom results (within a 1% difference) and you should only make decisions based on blossoms if you are close to a grand prize with few lanterns left at the end of the event based on how combinations/rounding out favors one chest. If you need 20 blossoms and have 120 lanterns left, just buy a gold chest rather than risk a chance of getting 0 lanterns back from 3 bronzes, as leftover blossoms do not matter. Obviously some examples won’t be so easy. Note that the chance of getting AT LEAST ONE daily prize with a certain # of lanterns left from a particular chest is not the same as averages, and therefore this math is most applicable to someone spending money on diamonds, or with bulks of diamonds, or just pouting their remaining lanterns on SoKs, etc. However, gold chests also give reno kits (and other stuff, but for me this is the only notable thing). For every 1 extra special daily you get from choosing bronze over gold, you will be sacrificing approximately 2.7-2.85 reno kits. Therefore I would recommend bronze to someone only concerned with daily specials’ average cost, or that needs observatory BPs. If 3 reno kits sound better to you than 1 SoK or w/e, you might want to stick with gold. If you need only 1 of a building to complete the set and have few lanterns left, I’m not sure this math will apply to you, as higher averages gained with less cost but more chests opened will have less of an advantage or even a disadvantage for calculating the chance of at least one daily being found, given that some of the average for the cheap chests comes from having a high # of specials found that would be impossible with few chests. See the example at the beginning of the next paragraph if interested. Feel free to skip the next paragraph if you are only concerned with average costs and don’t need to differentiate that from average chance of getting at least one more daily to fill a set. An example of my last point and a start to my longer post: Imagine a simple case with no trees or lantern return. Chest A has a 25% chance of returning a special and costs 100 hairballs. Chest B has a 5% chance of a special and costs 20 hairballs. You have 400 hairballs so you can open 4x chests with a 25% chance each or 20x chests with a 5% chance each. Your average return is 1 daily. But in case A you have a 31.64% chance of getting 0 specials (.75^4) while in case B that rises to 35.84% (.95^20). This makes sense since they have the same average, yet some of case B’s average comes from cases where there are 5+ specials, impossible in case A. This is not to say that in our event gold chests are better for this purpose, because in this example, the averages were the same, while in our event, bronze’s average is higher, so it could be reduced but still better. But I just want to stress the differences between averages, medians, chances of getting at least one daily, etc. Also there are looking theoretical examples with plentiful lanterns; if you have few lanterns left, you might want to look at combinations most likely to avoid ending up with leftover, unusable lanterns, as this will become more critical than these differences in averages. ok…now on averages in this event… An advantage between chests for blossoms is miniscule and should probably not go into your decision making: <1% in either direction depending on my # used for average lanterns from trees. You are better off only concerning yourself with this if you have few lanterns left and are very close to your next grand prize by how thing will round off, as stated above. Bronze chests are superior for average cost of special, by approximately 11 (or 12)% (a ratio of 1:1.11), so for every 9 dailies you get from gold, you will get about 10 from bronze. A significant, if not huge, difference. Where are you guys getting the 2.7# for lanterns from trees? I originally 2.45 # in my estimated calculations, but that might be wrong. I took a sample over a couple hundred trees (I know this is too small) and it looked like 50%-30%-19%-1% was a likely spread, which would be 2.45%. I’m less sure about the last two numbers, though. I could see them being as low as 15% and as high as 5% respectively, which would change things slightly. My other best guess from my data would be 50-30-15-5, which would be 2.65 on average, so in that case you guys might be right. Liam, I think you counted the bonus lanterns from bronze twice, effectively. Applying what you call “normalization” and increasing the percentages for prizes as if lanterns wasn’t a prize, after already counting the reduced cost from those lanterns is overkill. It’s either/or in calculations, I believe. In my math is calculate the same cost for chests as you (before trees), but I calculate the cost on average per chest AFTER 100 chests are opened and the lanterns from those chests have been received, and therefore those lantern return chests are a very real chunk of the sample. Bronze chests are still good, but with your math plus return from trees they would be ridiculous enough to outweigh even consideration for gold from those liking reno kits, for example (in my opinion) I’ll post my math below. Calculating average cost of chest AFTER lanterns returned from chests but not yet trees, and with plentiful supply so no problems from leftover unusable lanterns screwing you: Bronze, opening 100 chests costs 4,000 lanterns, 20x return of 70 lanterns=1,400 lanterns returned with a total cost of 2,600 lanterns, or 26 lanterns/ bronze chest. Gold, opening 100 chests cost 12,000 lanterns, 12x return of 200 lanterns=2,400 lanterns returned, with a total cost of 9,600 lanterns, or 96 lanterns/gold chest. Each chest also gives a tree-assuming the trees are the same on average, this favors bronze as more trees are given for the same # of lanterns spent. My 2 most likely predicted spreads for trees are 50% 1 lantern/30% 3 lanterns/19% 5 lanterns/1% 10 lanterns, for an average of 2.45 lanterns per tree OR 50-30-15-5, for an average of 2.65 lanterns per tree. If the 2.7ish number people are using is in fact, correctish, I am guessing it is actually 2.65 because of the convenience of this spread, and my data looks like it could support either one of these spreads. (Unless someone has hard data/facts saying 2.7 is in fact correct) To calculate the benefits of trees, I’ll show the math for 1 case, and then my results for the rest (with the same steps you can do yourself). Bronze chests=26 cost per chest-2.45 lanterns from tree=actual cost of 23.55 per chest. 100/7 (chance of daily) X 23.55=336.43 lantern cist per daily with bronze chests and trees=2.45 23.55/5=4.71 lantern cost per blossom. Do the same for gold, with trees=2.45: Bronze daily cost:336.43, Blossoms: 4.71 lanterns per blossom or .2123 blossoms/lantern Gold daily cost: 374.2, Blossoms: 4.6775 lanterns per blossom of .2138 blossoms/lantern Daily ratio of 1:1.1123 gold specials to bronze (advantage for bronze) Blossom difference: approximately .007, or less than 1%, in favor of gold Now for trees=2.65 lanterns! Bronze daily cost: 333.57, Blossoms: 4.67 lanterns per blossom or .2141 blossoms/lantern Gold daily cost:373.4, Blossoms: 4.6675 lanterns per blossom or .2142 blossoms/lantern Daily ratio of 1:1.1194 advantage for bronze, slightly larger than before (almost 12%!) Blossom difference: Basically identical, although technically gold is advantaged. If 2.7 is used the blossoms instead technically favor bronze, although again the numbers are basically identical For determing the ratio of dailies gained for reno kits lost: There is 8% value reno for every 25% value of the daily. With our 2.45 tree number, we gain an extra .1123 value of the special by using bronze, and with the 2.65 # we get an extra .1194. We can think of these as values of 2.8075 and 2.985 respectively by multiplying them by 25. We determine the ratio by then dividing 8 (for the 8% reno) by these extra daily % chance values, giving us values of 2.8495 reno kits lost per daily gained with the 2.45 tree #, or 2.68 reno kits lost per daily gained with the 2.65 #. So if 3 reno kits sound better than 1 daily, you probably should go gold. Please anyone feel free to correct me on anything I may be wrong about, I certainly may have made a mistake, or many. Also any input/math on what is actually best for getting AT LEAST ONE daily would probably the most practical advice for a lot of people on this board that is still not that covered (Including trying to avoid ending with 30 unusable lanterns based on combinations, etc. …this might be too complicated/require individual cases)